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## Über dieses Buch

This book offers students, scientists, and engineers an extensive introduction to the theoretical fundamentals of digital communications, covering single-input single-output (SISO), multiple-input multiple-output (MIMO), and time-variant systems. Further, the main content is supplemented by a wealth of representative examples and computer simulations.

The book is divided into three parts, the first of which addresses the principles of wire-line and wireless digital transmission over SISO links. Digital modulation, intersymbol interference, and various detection methods are discussed; models for realistic time-variant, wireless channels are introduced; and the equivalent time-variant baseband system model is derived. This book covers two new topics such as blockwise signal transmission and multicarrier modulation with orthogonal frequency-division multiplexing (OFDM) systems.

Since not all readers may be familiar with this topic, Part II is devoted to the theory of linear time-variant systems. The generalized convolution is derived, and readers are introduced to impulse response, the delay spread function, and system functions in the frequency domain. In addition, randomly changing systems are discussed. Several new examples and graphs have been added to this book.

In turn, Part III deals with MIMO systems. It describes MIMO channel models with and without spatial correlation, including the Kronecker model. Both linear and nonlinear MIMO receivers are investigated. The question of how many bits per channel use can be transmitted is answered, and maximizing channel capacity is addressed. Principles of space–time coding are outlined in order to improve transmission quality and increase data rates. In closing, the book describes multi-user MIMO schemes, which reduce interference when multiple users in the same area transmit their signals in the same time slots and frequency bands.

## Inhaltsverzeichnis

### Chapter 1. Transmission System with Quadrature Amplitude Modulation

Abstract
This chapter presents an overview on the principles of digital communications. We focus on a system with one transmitter and one receiver, i.e. for a channel with a single input and a single output (SISO). This will also provide the necessary basics for multiple input multiple output (MIMO) systems investigated in Part III. Depending on the characteristics of the transmission medium we have to differentiate between a wire-line and a wireless connection. Both channel types exhibit different properties and therefore will be treated separately. We start with the wire-line transmission link and in Chap. 4 the wireless system will be discussed in detail.
Joachim Speidel

### Chapter 2. Intersymbol Interference and Noise

Abstract
With the help of the discrete-time equivalent baseband system model we can now get insight into the two major impairments a signal incurs from the transmitter to the receiver, namely intersymbol interference and noise. For that purpose we separate the term for $$m=k$$ from the sum in (1.​40) and obtain
\begin{aligned} q(k)=a(k)h(0)+\sum _{\begin{array}{c} m=-\infty \\ m\ne k \end{array}}^{\infty }a(m)h\left( k-m\right) +n(k) \end{aligned}
We see that the receive sample q(k) is composed of the transmit symbol a(k) multiplied by h(0) of the discrete-time impulse response h(k), the distortion term
\begin{aligned} I(k)=\sum _{\begin{array}{c} m=-\infty \\ m\ne k \end{array}}^{\infty }a(m)h\left( k-m\right) \end{aligned}
and the noise n(k).
Joachim Speidel

### Chapter 3. Detection MethodsDetection methods

Abstract
In the following a survey on the most important detection methods is presented. We differentiate in principle between the symbol-by-symbol and the sequence or sequential detection. With the first method the receive signal q(k) in Figs. 1.​1 and 1.​5 is decided at every time instant k.
Joachim Speidel

### Chapter 4. Digital Transmission over Wireless, Time-Variant Channels

Abstract
Digital signal transmission over a wireless channel has become an important field due to the high flexibility and comfort of wireless connections for many users with the motto “telecommunications anytime and anywhere”. Therefore, in the following chapters we describe the principles of such systems and their design in some detail. A significant part is devoted to the wireless channel. The parameters of electrical cables or optical fibers are approximately constant over time. Consequently, they have been characterized as time-invariant and described by an impulse response $$g_{c}(t)$$ in Fig. 1.​1 of Sect. 1.​2. As we will see in detail, a wireless channel is significantly different and multifaceted.
Joachim Speidel

### Chapter 5. Basic Parameters of Wireless Transmission and Multipath Propagation

Abstract
In this chapter we summarize the main facts, which characterize a single input single output wireless link. Such channels can be partitioned into different segments. The inner part is the wave propagation channel, which is characterized by the free space between the output of the transmit antenna and the input to the receive antenna. The next level includes the characteristics of the transmit and the receive antenna, such as radiation pattern and antenna gains.
Joachim Speidel

### Chapter 6. Block-Wise Signals with/without Prefix Over FIR Channels

Abstract
In the following we consider channels, which can be modeled by a causal impulse response with finite duration, what we call finite impulse response (FIR) $$h(n)={\left\{ \begin{array}{ll}\begin{array}{ccc} h_{n} &{} ; &{} n=0,1,\ldots ,L\\ 0 &{} ; &{} else \end{array}&;\,\,\,\,\,h_{L}\ne 0\end{array}\right. }$$ We say, h(n) owns the length $$L+1$$, which is also the dimension of a corresponding signal vector. The channel parameters $$h_{n}$$ shall be time-invariant. n represents discrete time. All properties of FIR filters known from signal processing apply. Furthermore, we study discrete-time input signals with finite duration, which can be described by a signal vector also called block of samples. Long signals will be structured block-wise and the principle of block-wise transmission is discussed in quite detail. Finally, we introduce a guard interval between the signal blocks by means of a prefix or a cyclic prefix and study important properties.
Joachim Speidel

### Chapter 7. Multicarrier Modulation and OFDM

Abstract
The division of a frequency band into dedicated channels by modulation, called frequency-division multiplexing (FDM), has a long history. Prominent examples are the analog telephone networks until the 1970s. They were replaced by digital telephony, operating with time-division multiplex (TDM), in which dedicated time slot are allocated to each application. Moreover, the analog and later the digital television broadcasting networks—terrestrial, satellite and cable based—operate with FDM. Most mobile and cellular networks today utilize combinations of FDM and TDM.
Joachim Speidel

### Chapter 8. Introduction and Some History

Abstract
Time-variant systems are of general interest, because they play an important role in communications due to the emerging wireless networks for in-house and outdoor applications. As a matter of fact a wireless channel can change its parameters with time depending on the position of the mobile transmitter, the receiver, and on the change of the surroundings. During the education of electrical engineers the main focus is on time-invariant systems and the topic of time-variant systems is not always strongly alluded. Thus, also from this perspective a general view on time-variant systems and their mathematical description is favorable.
Joachim Speidel

### Chapter 9. System Theoretic Approach for the Impulse Response of Linear Time-Variant Systems

Abstract
Let $$\mathcal {T}[\ldots ]$$ be a linear system operator, which maps the input signal x(t) of a linear dynamic system to an output signal y(t).
Joachim Speidel

### Chapter 10. Properties of Time-Variant Convolution

Abstract
In this chapter we proof some important properties of the time-variant convolution in detail. The results are also summarized in Tables 10.1 and 10.2.
Joachim Speidel

### Chapter 11. System Functions and Fourier Transform

Abstract
We have already discussed the time-variant impulse response w(ts) and the delay spread function $$g(t,\tau )$$, which characterize a linear time-variant system completely and hence are called system functions. Now we will see that the latter provides meaningful Fourier transforms for applications in electrical engineering and thus system functions in the frequency domain. In the following sections we will apply the Fourier transform with respect to the variables t and/or $$\tau$$.
Joachim Speidel

### Chapter 12. Randomly Changing Time-Variant Systems

Abstract
Hitherto we have considered signals and characteristic functions of time-variant system, in particular the delay spread function $$g(t,\tau )$$, as deterministic. With the Fourier transform different spectra or transfer functions, such as the Doppler spread function $$G(f_{t},f_{\tau })$$, have been defined. In many applications, e.g., wireless communications the time-variant channel can take on a fast of different characteristics depending on the environment, the speed of the transmitter or receiver, and other effects. Hence, there is a need for the introduction of a statistical description for the most important system parameters.
Joachim Speidel

### Chapter 13. Principles of Multiple Input Multiple Output Transmission

Abstract
After the first demonstrations of electromagnetic waves in the year 1887 by the physicist Heinrich Hertz at the Technical University of Karlsruhe in Germany wireless telegraphy transmission was demonstrated at the end of the 19th century by the radio pioneer and founder of the later company Guglielmo Marconi.
Joachim Speidel

### Chapter 14. Principles of Linear MIMO Receivers

Abstract
As depicted in the block diagram of Fig. 14.1, we consider a MIMO system with frequency flat and in general time-varying channel with channel matrix $$\varvec{\mathrm {H}}(k)\,\epsilon \,\mathbb {C}^{N \times M}$$, input signal vector $$\varvec{\mathrm {s}}(k)\,\epsilon \,\mathbb {C}^{M \times 1}$$, noise vector $$\varvec{\mathrm {n}}(k)\,\epsilon \,\mathbb {C}^{N \times 1}$$, and receive vector $$\varvec{\mathrm {r}}(k)\,\epsilon \,\mathbb {C}^{N \times 1}$$.
Joachim Speidel

### Chapter 15. Principles of Nonlinear MIMO Receivers

Abstract
As we have seen in the previous chapter, a linear receiver tries to reduce the impact of inter-channel interference and partially of the noise in the receive signal $$\mathbf {y}(k)$$ of Fig. 14.​1.
Joachim Speidel

### Chapter 16. MIMO System Decomposition into Eigenmodes

Abstract
In this chapter we allude to a topic, which gives quite some inside into the functionality of a MIMO system. As we have seen, the MIMO channel matrix $$\mathbf {H}(k)$$ introduces inter-channel interference to the receive signal
\begin{aligned} \mathbf {r}(k)=\mathbf {H}(k)\mathbf {s}(k)+\mathbf {n}(k) \end{aligned}
We are now interested in the decoupling of the receive signal. To achieve this goal $$\mathbf {H}(k)$$ has to be transformed into a matrix, in which only one diagonal is covered by entries unequal to zero and all remaining elements have to be zero. In the following we drop the discrete time k to simplify the notation.
Joachim Speidel

### Chapter 17. Channel Capacity of Single-User Transmission Systems

Abstract
In this chapter, we allude to a topic which is important for the design of a communications system. We will answer the question how many bit/s can be transmitted per symbol or equivalently per channel use. For a certain bandwidth of the channel the interesting point is how many bit/s per Hz bandwidth can be achieved as a maximum. The channel capacity was introduced by Shannon in his pioneering work [1] in the year 1948 for single input single output (SISO) channels. The extension to MIMO channels was given by Telatar [2]. The capacity of various models for stochastic MIMO channels have been intensively studied, e.g., in [3].
Joachim Speidel

### Chapter 18. MIMO Systems with Precoding

Abstract
In Chap. 14 we have investigated the zero-forcing and the minimum mean squared error (MMSE) receiver, which are able to remove or at least minimize the inter-channel interference to the expense of a potential increase of the mean noise power at the receiver output. To maximize the channel capacity we have already investigated a prefilter in Chap. 17, which acts as a power allocation filter at the transmitter. Now we are going to consider prefilters also denoted as precoders to reduce inter-channel interference and thus move the receive filter in principle to the transmitter.
Joachim Speidel

### Chapter 19. Principles of Space-Time Coding

Abstract
Figure 19.1 shows the principle block diagram of a MIMO transmitter with space-time encoding. The incoming bit sequence b(n) is fed into the QAM mapper, which periodically maps $$\kappa$$ consecutive bits to a QAM symbol $$c(k')$$, constituting a $$2^{\kappa }$$-ary QAM. b(n) may contain redundancy bits from a forward error correction encoder, [1, 1].
Joachim Speidel

### Chapter 20. Principles of Multi-user MIMO Transmission

Abstract
Hitherto, we have considered the MIMO transmission between a base station and one user, which we call single-user MIMO transmission. In a communications network the base station has to serve a large number of users, e.g., in an in-house area with a wireless local area networks (WLAN) according to the standard IEEE 802.11. Also in outdoor scenarios a multitude of users has to be addressed with the cellular networks of the type 3G (year 2004), 4G (year 2010), and 5G (year 2020) with data rates of about 8 Mbit/s, 100 Mbit/s, and up to 1 Gbit/s, respectively. In this Chapter we investigate methods for data communication between the base station and the users. Each transmitter and receiver shall be equipped with multiple antennas to benefit from the MIMO principle, which we call multi-user MIMO (MU MIMO) transmission. Also in the case that each user equipment has only one antenna, the term MIMO is used, because the antennas of all users taken together are considered as multiple input or multiple output. We differentiate between the directions from the base station to the users called the downlink and between the link from the users to the base station, which is referred to as uplink. Conventionally, without the MIMO principle the base station allocates certain time slots or frequency bands to the users. With multiple antennas a multi-user MIMO scheme can serve all users at the same time and in the same frequency band, hence providing a higher efficiency. While the WLAN standards IEEE 802.11 a, b, g, and n do not support multi-user MIMO techniques, the later versions AC-WLAN or AC Wave 2 own these benefits.
Joachim Speidel

### Backmatter

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